Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.
The measure of the third side could be __, __, or __.
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 6 and 2, we can determine the possible measures of the third side by examining which combinations satisfy the Triangle Inequality Theorem:
1. For the third side to be longer than the difference between the other two sides, it must be less than 6+2 = 8.
2. For the third side to be shorter than the sum of the other two sides, it must be greater than 6-2 = 4.
Therefore, the possible whole number measures of the third side in ascending order are 5, 6, and 7.